Abstract: A tapping machine (10), for tapping perforated products such as nuts (14), bushings or the like, comprises a spindle (11) on the longitudinal axis (12) of which a tapping tool (13) is rotatably mounted which tapping tool (13) is provided with a stem (21) having a longitudinal axis and a head having a threading to be inserted inside an appropriate hole provided in a nut (14) to be threaded, as well as pusher devices (16) for pushing a nut (14) against the threading surface of the tapping tool (13). Said machine further comprises an anti-vibration centring group (19) which acts on the stem of the tapping tool (13), substantially constraining the tapping tool (13) in a radial direction, preventing a de-alignment of the longitudinal axis (12) of the stem of the tapping tool and maintaining freedom of rotation thereof. Said anti-vibration centring group (19) is selectively movable along the stem of the tapping tool (13) in a parallel direction to the longitudinal axis of said stem (21).